Clifford Algebra to Geometric Calculus
Clifford Algebra to Geometric Calculus

Author: David Hestenes

Publisher: Springer Science & Business Media

Published: 1984

Total Pages: 340

ISBN-13: 9789027725615

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Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Nilpotence and Periodicity in Stable Homotopy Theory
Nilpotence and Periodicity in Stable Homotopy Theory

Author: Douglas C. Ravenel

Publisher: Princeton University Press

Published: 1992-11-08

Total Pages: 228

ISBN-13: 9780691025728

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Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

On Thom Spectra, Orientability, and Cobordism
On Thom Spectra, Orientability, and Cobordism

Author: Yu. B. Rudyak

Publisher: Springer Science & Business Media

Published: 2007-12-12

Total Pages: 593

ISBN-13: 3540777512

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Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.

Organic Chemistry I For Dummies
Organic Chemistry I For Dummies

Author: Arthur Winter

Publisher: John Wiley & Sons

Published: 2016-05-13

Total Pages: 472

ISBN-13: 1119296579

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Organic Chemistry I For Dummies, 2nd Edition (9781119293378) was previously published as Organic Chemistry I For Dummies, 2nd Edition (9781118828076). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. The easy way to take the confusion out of organic chemistry Organic chemistry has a long-standing reputation as a difficult course. Organic Chemistry I For Dummies takes a simple approach to the topic, allowing you to grasp concepts at your own pace. This fun, easy-to-understand guide explains the basic principles of organic chemistry in simple terms, providing insight into the language of organic chemists, the major classes of compounds, and top trouble spots. You'll also get the nuts and bolts of tackling organic chemistry problems, from knowing where to start to spotting sneaky tricks that professors like to incorporate. Refreshed example equations New explanations and practical examples that reflect today's teaching methods Fully worked-out organic chemistry problems Baffled by benzines? Confused by carboxylic acids? Here's the help you need—in plain English!

Foundations of Module and Ring Theory
Foundations of Module and Ring Theory

Author: Robert Wisbauer

Publisher: Routledge

Published: 2018-05-11

Total Pages: 622

ISBN-13: 1351447343

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This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

March's Advanced Organic Chemistry
March's Advanced Organic Chemistry

Author: Michael B. Smith

Publisher: John Wiley & Sons

Published: 2007-01-29

Total Pages: 2379

ISBN-13: 0470084944

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The Sixth Edition of a classic in organic chemistry continues its tradition of excellence Now in its sixth edition, March's Advanced Organic Chemistry remains the gold standard in organic chemistry. Throughout its six editions, students and chemists from around the world have relied on it as an essential resource for planning and executing synthetic reactions. The Sixth Edition brings the text completely current with the most recent organic reactions. In addition, the references have been updated to enable readers to find the latest primary and review literature with ease. New features include: More than 25,000 references to the literature to facilitate further research Revised mechanisms, where required, that explain concepts in clear modern terms Revisions and updates to each chapter to bring them all fully up to date with the latest reactions and discoveries A revised Appendix B to facilitate correlating chapter sections with synthetic transformations